Editing Hypercube (section)

== Related families of polytopes ==
The hypercubes are one of the few families of [[regular polytope]]s that are represented in any number of dimensions.<ref>{{cite journal|url=https://dx.doi.org/10.1016/0166-218X%2892%2990121-P|title=Transmitting in the n-dimensional cube|author1=Noga Alon|journal=Discrete Applied Mathematics |date=1992 |volume=37-38 |pages=9–11 |doi=10.1016/0166-218X(92)90121-P }}</ref>

The '''hypercube (offset)''' family is one of three [[regular polytope]] families, labeled by [[Coxeter]] as ''γ<sub>n</sub>''. The other two are the hypercube dual family, the '''[[cross-polytope]]s''', labeled as ''β<sub>n,</sub>'' and the '''[[simplex|simplices]]''', labeled as ''α<sub>n</sub>''. A fourth family, the [[hypercubic honeycomb|infinite tessellations of hypercubes]], is labeled as ''δ<sub>n</sub>''.

Another related family of semiregular and [[uniform polytope]]s is the '''[[demihypercube]]s''', which are constructed from hypercubes with alternate vertices deleted and [[simplex]] facets added in the gaps, labeled as ''hγ<sub>n</sub>''.

''n''-cubes can be combined with their duals (the [[cross-polytope]]s) to form compound polytopes:

* In two dimensions, we obtain the [[octagram]]mic star figure {8/2},
* In three dimensions we obtain the [[compound of cube and octahedron]],
* In four dimensions we obtain the compound of tesseract and 16-cell.